Entropy Dissipation and Long-Range Interactions

By Radjesvarane Alexandre, Laurent Desvillettes, Cédric Villani, B. Wennberg. 2000

289 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/a4dd3720c3e53303a68cc313fc4fe7483fc5343c

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In Applied Mathematics

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Citations in the corpus

Explicit Coercivity Estimates for the Linearized Boltzmann and Landau Operators (2006, background): “Indeed, for Coulombian interactions the Boltzmann collision operator does not make sense anymore (see Villani, 2000, Annex I, Appendix).”
Chapter 2 – A Review of Mathematical Topics in Collisional Kinetic Theory (2002, methodology): “In particular, for the Landau equation with Coulomb potential (γ = −3 in dimension N = 3), nothing is known beyond existence of weak solutions (see Villani [446] or the remarks in [10]).”
The weak Harnack inequality for the Boltzmann equation without cut-off (2016, methodology): “The term Q2pf, gq is of lower order because of the cancellation lemma [62],[1].”
On the Boltzmann equation for long‐range interactions (2002, background): “At this point we invoke the results that we have established together with Desvillettes and Wennberg in [6].”
Global Existence and Full Regularity of the Boltzmann Equation Without Angular Cutoff (2009, methodology): “3) and the cancellation lemma from [6], we get”
Classical Solutions to the Boltzmann Equation for Molecules with an Angular Cutoff (2003, background): “Therefore, the right-hand side in (99) is uniformly bounded in L 2 ([0, 1 ]× T 3 × R 3 ). By the averaging lemma [7], it follows that”
Regularizing Effect and Local Existence for the Non-Cutoff Boltzmann Equation (2009, methodology): “For R1, according to the cancellation lemma, Corollary 2 of [6], we have R1 = 1 2 ∫”
On the Landau approximation in plasma physics (2004, methodology): “The present study rests on recent developments in the study of grazing collisions for the Boltzmann equation: 1) a precise understanding of regularizing effects associated with the entropy production, which were studied in our joint work [2] with Desvillettes and Wennberg (what we call entropy produ”